Does Blender support importing/exporting REDlog color format?
Not as video, given that Blender will only import video at a down bitted 8 bits per channel, and potentially dubiously at that.

If you export to a proper still format such as a TIFF, not DPX as Blender's DPX code has been horribly broken for years, you can. This would require an OCIO stanza to properly convert it to the reference space.

Other option is to output a scene referred linear EXR with REC.709 primaries, or in the native RED gamut and write a simple OCIO stanza to handle the conversion.


  can REDlog video/color be preserved when imported into Blender (as the
  effect background) and exported with the effect applied as an image
  sequence?


It is impossible to preserve a wider gamut in a smaller gamut if you intend to conduct any manipulations on the pixels. This is a bit of a tricky area so I'll leave it at that to avoid boring you into submission. By default, Blender uses a REC.709 based reference space, and almost every single camera sensor on the market can record a wider gamut than the REC.709 / sRGB reference lights can represent. The only way around this is to use a wider reference space, and that is another topic altogether.